Trig sin cos and tan angle circle: tan(4pi/3), cos(11pi/6), sin(5pi/4) in Q1
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Dr.Peterson
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Here's a more readable image:
Question 2 is asking you to fill in the blanks with an angle in the first quadrant (that is, between 0 and pi/2 radians) with the same tangent as 4pi/3, and one with the same cosine as 11pi/3, and one with the same sine as 5pi/4.
Now, what do you know about these functions that you can use to determine that? (One of them actually can't be done, because the function value is negative, and all trig functions in the first quadrant are positive.)
Now, I'm curious about what "c" as a superscript means. How was that defined in your class? It looks like it's supposed to mean "radians"; but if so, why?
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blamocur
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Looks like you mean question 2.
BigBeachBanana
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It’s actually a symbol for an arc. More specifically, length of the arc of the unit circle.
So is
240 right for the first one?
Steven G
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Of course this not correct. The problem asked for an answer between 0 and pi/2. Forgetting units (like degrees and radians) pi/2 is about 1.5. 240 is 160 times 1.5 so no way is 240 between 0 and pi/2.
Onto units: When they say that the answer should be between 0 to 2pi, then they mean that the units are in radians since they did NOT mention any units. The 240 which you mentioned is in degrees so even if 240 was between 0 and pi/2 that would be the incorrect answer.
What is true is that 4pi/3 (= 4pi/3 radians) = 240 degrees. So you did convert 4pi/3 radians to 240 degrees correctly, but that is not what was asked of you.
They are asking you to find an angle t, in radians, in the 1st quadrant, where tan(t) = tan(4pi/3).
Hint: think reference angles.
Show us some work or explain where you are stuck if you want help from this forum. Draw a diagram of what they are asking for and what is given. Good luck!
Harry_the_cat
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Have you learnt what is commonly called the CAST rule?
That is partially complete (and correct).
To proceed further, use:
tan ( 180º + Θ ) = tan(Θ) where 0 ≤ Θ ≤ 90°
Dr.Peterson
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I did a search; at least one site said it's used mostly in India, and another said the symbol is an arc rather than a c (though I found none that show it that way); but most call it the letter c, and many say it stands for "circular measure".
Here is what Wikipedia says:
The International Bureau of Weights and Measures and International Organization for Standardization[8] specify rad as the symbol for the radian. Alternative symbols that were in use in 1909 are c (the superscript letter c, for "circular measure"), the letter r, or a superscript R, but these variants are infrequently used, as they may be mistaken for a degree symbol (°) or a radius (r). Hence an angle of 1.2 radians would be written today as 1.2 rad; archaic notations could include 1.2 r, 1.2rad, 1.2c, or 1.2R.
In mathematical writing, the symbol "rad" is often omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant, the degree sign ° is used.
I guess it's worth knowing about; I don't think I'd seen it.
I think it's clear they want an angle in radians, and in the first quadrant; 240 is neither.
It's possible that they are really asking for the reference angle, which is always in the first quadrant.