Tan θ = 4/3 where 0<θ<90° find cos 2θ

Question

Find the exact value

Answer 1

Using Trig double angle identities...

 

cos (2θ) = cos² θ - sin² θ which is also 2 cos² θ -1.

 

Let's try both so we can check.

From tan θ = 4/3, this gives a ratio of 4 to 3 for opposite to adjacent sides. Using Pythagorean theorem (sorry don't know logic presented in your class so flying through this part), hypotenuse is square root of 4*4 +3*3 is square root of 25 = 5.

sin θ is 4/5 and cos θ is 3/5.

 

Using first identity 9/25 - 16/25 is -7/25.

Using second identity to check is 18/25 - 1 is -7/25. Check good.

 

Good luck, TV