Question

how do i find the exact value of the trigonometric function -> cos 9π/4

Answer 1

\(\cos(\dfrac{9\pi}{4})=\cos(\dfrac{9\pi}{4}-2\pi)=\cos(\dfrac{\pi}{4})=\ ?\)

Answer 2

just to elaborate:

pi/4 = pi/4 * 180/pi = 180/4 = 45 degrees

we multiply bu 180/pi to change from radians to degrees since 1 pi radians = 180 degrees

and you know that 45-45-90 triangle has side ratios of 1, 1, sqrt(2)

and you should know the following:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = sin/cos = opposite/adjacent

sec = 1/cos

csc = 1/sin

cot = 1/tan = cos/sin

Answer 3

Also the reason why 2pi was subtracted from 9pi/4 was because the cosine is a periodic function where the same value recurs every 2pi radians.

Answer 4

\[\cos \frac{ 9 \pi }{ 4 }=\cos \left( 2 \pi+\frac{ \pi }{ 4 } \right)=\cos \frac{ \pi }{ 4 }=?\]