Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. find cos(θ) and csc(θ).

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

we can substitute the value of sec(θ) in this equation:

and solve for for cos(θ)

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by

b) since right triangle is mentioned in the question. We can use:

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

we can find the third side using the Pythagoras theorem.

we can find the sin(θ) using this side:

and since

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

answer: about 22.67

step-by-step explanation: