Trigonometric functions

Question

let tanθ=square root of 3 over 5, find the other five trigonmetric functions. 

Answer 1

First, draw a right triangle where one of the acute angles is θ(theta). Since tangent is opposite/adjacent, the side opposite of theta will have length square root 3 and the side adjacent to theta (not the hypotenuse) will have length 5. Now, the hypotenuse is the only length you do not know. However, by the Pythagorean Theorem, if you let c be the length of the hypotenuse:

 

 (sqrt(3))^2+5^2=c^2. Solving this equation for c tells you that  c=sqrt(28) which is the same as c=2*sqrt(7) if you break down the square root.

 

Now that you know c, you can find the other trig functions knowing that

 

sine=opposite/hypotenuse

cosine=adjacent/hypotenuse

cosecant=1/sine

secant=1/cosine

cotangent=1/tangent