Trig

[123]

I need help to solve this:
Find \(\displaystyle 6sin(\pi +\alpha)+cos(\frac{\pi}{2}+\alpha)\), if \(\displaystyle cos\alpha=0,6\) and \(\displaystyle 0<\alpha<\frac{\pi}{2}\)

Thank you in advance! :mrgreen:

 

[galactus]

Note \(\displaystyle sin(\pi+\alpha)=-sin{\alpha}, \;\ cos(\frac{\pi}{2}+\alpha)=-sin\alpha\)

If \(\displaystyle cos\alpha=\frac{3}{5}\Rightarrow sin\alpha=\frac{4}{5}\)

Finish?.

 

[123]

Not sure. Answer is -5,6.
Any idea?

 

[galactus]

I given you everything but the outright answer. You can not see it now?.

Using the identities from my last post, it is easy to see that \(\displaystyle 6sin(\pi+\alpha)+cos(\frac{\pi}{2}+\alpha)=-7sin\alpha\)

and since \(\displaystyle sin\alpha=\frac{4}{5}\), then...................?

May I please suggest using a decimal point instead of a comma.

-5,6 should be -5.6

-5,6 looks like you are referring to two different values: -5 and 6.

 

[123]

I given you everything but the outright answer. You can not see it now?.

Using the identities from my last post, it is easy to see that \(\displaystyle 6sin(\pi+\alpha)+cos(\frac{\pi}{2}+\alpha)=-7sin\alpha\)

and since \(\displaystyle sin\alpha=\frac{4}{5}\), then...................?

May I please suggest using a decimal point instead of a comma.

-5,6 should be -5.6

-5,6 looks like you are referring to two different values: -5 and 6.

Ok. Thank You.