Find the values of the trigonometric functions of θ from the information given.

Question

cot(θ) = 8/9 ,  cos(θ) > 0

sin(θ)=

cos(θ)=

tan(θ)=

csc(θ)=

sec(θ)=

Answer 1

Using x instead of Θ because easier to type.

Given cot(x)=8/9, then tan(x)=9/8. Need to do this because arccot is not on your calculator.

Given cos(x)›0, then x is in Q1 or Q4.

So, x = atctan(9/8) ≈ ±48.35°.

Draw a right triangle in Q1 with base (adjacent) = 8 and height (opposite) = 9.

Use Pythagorean Theorem to compute hypotenuse ≈ 12.04.

Now you can find all six trig functions requested:

sin(x)≈±9/12, cos(x)≈8/12, csc(x)≈±12/9, sec(x)≈12/8, tan(x)=9/8, and cot(x)=8/9. QED