Find the six function values for pi/2-θ

Question

Given that sinθ=1/5 and that the terminal side is in quadrant II, give an exact answer for each of the six function values for pi/2-θ AND θ-pi/2.

(Simplify your​ answer, including any radicals. Use integers or fractions for any numbers in the​ expression.)

NOTE: I have found θ and it is 0.20135792, but I think the question does not want any decimals within the final answer, but when I plug this number, I get a decimal. I was just wondering if there are other ways I can get the answer but with no decimals. Thank you!

Answer 1

You are correct about no decimals expected.

You are told the ratio of the opposite to the hypotenuse is 1/5

Draw a terminal side in quadrant 2; drop a vertical line to the x axis to form a right triangle, and label the vertical side of the triangle 1 and the hypotenuse 5.

Pythagorean theorem tells you the horizontal side of the triangle has length square root of 24. But it's value is because you are in the second quadrant.

Therefore, cos(θ) = -sqrt(24) / 5.

Now use the angle sum (and difference) formulas

For example:

Cos (π/2 - θ) = cos(π/2)cos(θ) + sin(π/2)sin(θ)

= 0 -sqrt(24) / 5. + 1 ( 1/5 ) = 1/5