Stuck on 9 problems: cos (tan^-1 u + tan^-1 v), cos [sin^-1 2/3 + 2sin^-1 (-1/3)],...

[awdree]

Been reading my textbook and still dont get how to work out each problem with the given answer

1) cos (tan^-1 u + tan^-1 v)

answer:

2) cos [sin^-1 2/3 + 2sin^-1 (-1/3)]

answer:

3) sec (theta) = - 6 (square root) 11 divided by 11, csc (theta) greater than 0, find sin (2theta)

answer:

4) sin (theta) = - square root 5 divided by 5, 3pi divided by 2 < theta < 2pi, find cos (theta/2)

answer: -

5) sin (theta) = 4/5, 3pi/2 < theta < 2pi, find tan (2theta)

answer:

6) cos 5(theta) divided by 2 + cos 3(theta) divided by 2

answer: 2 cos(2θ) cos

7) What are the x intercepts of the graph of f(x)= 2 sin (3x)+ square root 3 on the interval [0,2pi]

answer:

,

,

,

,

,

8) If cos (theta) = 1/3, theta in quadrant IV, find the exact value of sin (theta + pi/3)

answer:

Lastly,

9) Given that f(x) =sin (x), g(x)= cos (x) + h(x) = tan (x), point (x,square root 3) on circle x^2+y^2=7, angle a quadrant II, point (-1/3, y), on circle x^2+y^2=1, angle B in quadrant III, find f(2a)

answer:

Again, I have the answers to the problems, I just want to know step by step on how to get the answer.

 

[stapel]

I've moved your pre-calculus posting from "Calculus" to one of the pre-calculus categories. Also, since we're not in your class, we don't have the login info for your images. You'll need to provide that information on your own. Sorry.

Been reading my textbook and still dont get how to work out each problem with the given answer

1) cos (tan^-1 u + tan^-1 v)

answer: https://alamo.instructure.com/courses/968472/files/69461235/preview

2) cos [sin^-1 2/3 + 2sin^-1 (-1/3)]

answer: https://alamo.instructure.com/courses/968472/files/69461296/preview

All you've posted are expressions. There are no instructions, so there is no actual "question" to "answer".

3) sec (theta) = - 6 (square root) 11 divided by 11, csc (theta) greater than 0, find sin (2theta)

answer: https://alamo.instructure.com/courses/968472/files/69461267/preview

Was the original question (complete with its instructions) something like the following?

. . . . .\(\displaystyle \mbox{Given that }\, \sec(\theta)\, =\, -\dfrac{6\, \sqrt{\strut 11\,}}{11}\, \mbox{ and that }\, \csc(\theta)\, >\, 0,\, \mbox{ find }\, \sin(2\theta).\)

If so, what have you tried? If not, what was the actual exercise? Either way, what have you tried? Where are you stuck?

4) sin (theta) = - square root 5 divided by 5, 3pi divided by 2 < theta < 2pi, find cos (theta/2)

answer: https://alamo.instructure.com/courses/968472/files/69461437/preview

This one looks very similar to Exercise (3), and likely works in much the same way.

5) sin (theta) = 4/5, 3pi/2 < theta < 2pi, find tan (2theta)

answer: https://alamo.instructure.com/courses/968472/files/69461329/preview

See Exercise (3).

6) cos 5(theta) divided by 2 + cos 3(theta) divided by 2

answer: 2 cos(2θ) cos https://alamo.instructure.com/courses/968472/files/69461230/preview

Are you maybe expected to "evaluate the expression" for some given value of "theta"? Or did the instructions specify something else? Either way, how far have you gotten?

7) What are the x intercepts of the graph of f(x)= 2 sin (3x)+ square root 3 on the interval [0,2pi]

answer: https://alamo.instructure.com/courses/968472/files/69461374/preview
https://alamo.instructure.com/courses/968472/files/69461431/preview
https://alamo.instructure.com/courses/968472/files/69461327/preview
https://alamo.instructure.com/courses/968472/files/69461251/preview
https://alamo.instructure.com/courses/968472/files/69461423/preview
https://alamo.instructure.com/courses/968472/files/69461231/preview

You set this equal to zero and... then what? (here)

8) If cos (theta) = 1/3, theta in quadrant IV, find the exact value of sin (theta + pi/3)

answer: https://alamo.instructure.com/courses/968472/files/69461404/preview

Did you try applying a trig angle-sum identity? If so, which one? How far did you get? If not, what method are you trying?

9) Given that f(x) =sin (x), g(x)= cos (x) + h(x) = tan (x), point (x,square root 3) on circle x^2+y^2=7, angle a quadrant II, point (-1/3, y), on circle x^2+y^2=1, angle B in quadrant III, find f(2a)

answer: https://alamo.instructure.com/courses/968472/files/69461404/preview

I'm not understanding the definition of g(x), nor why you need g(x), h(x), the points, the circles, or Angle B...? Is there maybe a picture that goes with this?

When you reply, please include a clear listing of your thoughts and efforts on each exercise, so we can see where you're bogging down. Thank you!

 

[pka]

All of those links are pass-word protected.

 

[awdree]

Figured two of them. I just need the steps on how to go about the problems.

Haven't tried figuring out the problems, been scrolling through my textbook to find examples and can't find anything similar to the problems to help me through them. They only show the answers, but I want to know how did they get the answers. Sorry about the answers not showing up, I had copied and pasted them from the website I am viewing my textbook from.

1) sec(theta)= - 6 square root 11/11, csc(theta) > 0, find sin(2theta)

the answer shows: -5 square root 11/18

2) sin(theta)= -square root 5/5, 3pi/2 < theta < 2pi, find tan(2theta)

the answer shows: - square root 5 + 2(square root)5 / 10

3) sin(theta)= 4/5, 3pi/2 < theta <2pi, find tan(2theta)

the answer shows: 24/7

4) cos (5theta)/2 + cos (3theta)/2 =

the answer shows: 2cos(2theta)cos(theta/2)

5) What are the x-intercepts of the graph of f(x)=2 sin(3x) + square root 3 on the interval [0,2pi]?

the answer shows: 4pi/9, 5pi/9, 10pi/9, 11pi/9, 16pi/9, 17pi/9

*there are no graphs shown on this problem

6) If cos(theta)=1/3, theta in quadrant IV, find the exact value of sin(theta+pi/3)

the answer shows: -2 square root 2 + square root 3/6

7) Given that f(x)= sin x, g(x)= cos x, and h(x)= tan x, evaluate the given function. The point (x, square root 3), on the circle x^2+y^2=7, also lies on the terminal side of an angle A in quadrant II. The point (-1/3, y), on the circle x^2+y^2=1, also lies on the terminal side of an angle B in quadrant III.

f(2a)

the answer shows: -4 square root 3/7




-I desperately want to know how they came up with the answers. I just want to know the step by step process of it all. Thank you so much again

 

[stapel]

1) cos (tan^-1 u + tan^-1 v)

2) cos [sin^-1 2/3 + 2sin^-1 (-1/3)]

Lacking the instructions, we still cannot advise on these. Sorry.

...been scrolling through my textbook to find examples and can't find anything similar to the problems to help me through them.... I desperately want to know how they came up with the answers.

It's very odd that your trig book and trig class covered so little actual trig! Since these topics weren't covered, you'll have to attempt self-study. We can provide you with some direction in that regard.

3) sec (theta) = - 6 (square root) 11 divided by 11, csc (theta) greater than 0, find sin (2theta)

the answer key shows: -5 square root 11/18

This exercise requires that you be familiar with the Pythagorean Theorem (here), the unit circle (here), and the basic trig ratios in all four quadrants (here). Study at least three lessons from each link before attempting this exercise.

4) sin (theta) = - square root 5 divided by 5, 3pi divided by 2 < theta < 2pi, find cos (theta/2)

the answer key shows: - square root 5 + 2(square root)5 / 10

5) sin (theta) = 4/5, 3pi/2 < theta < 2pi, find tan (2theta)

the answer key shows: 24/7

These work similarly to (3), but also require that you know, and know how to use, trig identities (here). Note: You'll need to memorize many of these identities; a good start would be the abbreviated listing here.

6) cos 5(theta) divided by 2 + cos 3(theta) divided by 2

the answer key shows: 2cos(2theta)cos(theta/2)

What were the instructions for this? Were you maybe supposed to "combine into one term, using identities"? If so, study at least three lessons from the link, and then try this. If not, please reply with the actual instructions.

7) What are the x intercepts of the graph of f(x)= 2 sin (3x)+ square root 3 on the interval [0,2pi]

the answer key shows: 4pi/9, 5pi/9, 10pi/9, 11pi/9, 16pi/9, 17pi/9

*there are no graphs shown on this problem

There doesn't need to be a graph. You learned, back in algebra, about x-intercepts of graphs being the same as the real-valued solutions to "f(x) = 0" (here); hence, the instructions provided earlier.

But now that we know that your class didn't cover the trig required for your assignment, we know that you probably haven't seen anything related to solving trig equations. So you'll need to try to teach yourself that, too. (here)

8) If cos (theta) = 1/3, theta in quadrant IV, find the exact value of sin (theta + pi/3)

the answer key shows: -2 square root 2 + square root 3/6

You'll need to know the basic reference-angle values (here). Use one of those values (but memorize the entire table or chart!), and apply a trig identity.

9) Given that f(x) =sin (x), g(x)= cos (x) + h(x) = tan (x), point (x,square root 3) on circle x^2+y^2=7, angle a quadrant II, point (-1/3, y), on circle x^2+y^2=1, angle B in quadrant III, find f(2a)

the answer key shows: -4 square root 3/7

Given only that f(x) = sin(x) and that Angle a is in the second quadrant, there is no way to find the value of f(2a). (This is why I'd asked you about any other information. Since you have not responded with that information, I'll guess it was missing, along with the chapters in the book and a month or two of classroom instruction.)

The above is easily more than one person can self-teach through online lessons. Your best bet (after complaining to the administration of your school about being tested over material that's never been mentioned in class) may be to hire a qualified local tutor, and set aside an hour or two a day for concentrated private instruction. With hard work and a little luck, you may be able to get caught up to the material in only a few weeks!

 

[awdree]

Okay, thank you for your time. I appreciate it greatly!

 

[Ishuda]

Haven't tried figuring out the problems, been scrolling through my textbook to find examples and can't find anything similar to the problems to help me through them. They only show the answers, but I want to know how did they get the answers. Sorry about the answers not showing up, I had copied and pasted them from the website I am viewing my textbook from.

1) sec(theta)= - 6 square root 11/11, csc(theta) > 0, find sin(2theta)

the answer shows: -5 square root 11/18

2) sin(theta)= -square root 5/5, 3pi/2 < theta < 2pi, find tan(2theta)

the answer shows: - square root 5 + 2(square root)5 / 10

3) sin(theta)= 4/5, 3pi/2 < theta <2pi, find tan(2theta)

the answer shows: 24/7

4) cos (5theta)/2 + cos (3theta)/2 =

the answer shows: 2cos(2theta)cos(theta/2)

5) What are the x-intercepts of the graph of f(x)=2 sin(3x) + square root 3 on the interval [0,2pi]?

the answer shows: 4pi/9, 5pi/9, 10pi/9, 11pi/9, 16pi/9, 17pi/9

*there are no graphs shown on this problem

6) If cos(theta)=1/3, theta in quadrant IV, find the exact value of sin(theta+pi/3)

the answer shows: -2 square root 2 + square root 3/6

7) Given that f(x)= sin x, g(x)= cos x, and h(x)= tan x, evaluate the given function. The point (x, square root 3), on the circle x^2+y^2=7, also lies on the terminal side of an angle A in quadrant II. The point (-1/3, y), on the circle x^2+y^2=1, also lies on the terminal side of an angle B in quadrant III.

f(2a)

the answer shows: -4 square root 3/7




-I desperately want to know how they came up with the answers. I just want to know the step by step process of it all. Thank you so much again

A bit more of a hint for
3) sec (theta) = - 6 (square root) 11 divided by 11, csc (theta) greater than 0, find sin (2theta)

For right triangles
sec = hypotenuses over adjacent and since
\(\displaystyle sec(\theta)\, =\, -\frac{6\, \sqrt{11}}{11}\, =\, \frac{6\, \sqrt{11}}{-11}\)
we have a right triangle similar to
hypotenuses = \(\displaystyle 6\, \sqrt{11}\),
adjacent = \(\displaystyle -11\),
which means the angle is in the 2nd or 3rd quadrant. Since \(\displaystyle csc(\theta)\) is positive, we have the angle is in the second quadrant and, by the Pythagorean Theorem we have
opposite = \(\displaystyle 5\, \sqrt{11}\).
You should now be able to calculate all needed trig functions for the angle.

So use the double angle formula to compute \(\displaystyle sin(2\,\theta)\)

 

[awdree]

Thank you so much Ishuda. Youre an absolute blessing