Question

Select the correct answer from each drop-down menu. Identify the exact value of the trigonometric functions sin x and cos x. If x is an acute angle and tan x = 5, The value of sin x = The value of cos x =sin x= A. 1/sqrt(26) B. 6/26 C. 3/13cos x= A. 1/sqrt(26) B. 6/26 C. 3/13

Answer 1

Since we know that tanx=5, we can find the angle easily using the inverse function:

$\begin{gathered} \tan x=5 \\ \Rightarrow x=\tan ^{-1}(5)=78.69 \\ x=78.69 \end{gathered}$

We have then that the angle is x = 78.69°, now we only find the value of cosine and sine:

$\begin{gathered} \cos (78.69)=0.196116\approx\frac{1}{\sqrt[]{26}} \\ \sin (78.69)=0.980581\approx\frac{5}{\sqrt[]{26}} \end{gathered}$

therefore, sinx=5/sqrt(26) and cosx=1/sqrt(26)