Trigonometry
Angle Sum and Difference, Double Angle and Half Angle Formulas
Find the exact value of:
If sinx = 4/8, find Cos (6x)

3√3

Step-by-step explanation:

If sinx = 4/8, find Cos (6x)

we need to first find cos

but applying trigonometry rule

sin²x+cos²x = 1

sinx = 4/8

sin²x = (4/8)² = 4²/8² = 16/64

from the rule

cos²x= 1 -sin²x = 1-16/64 = 64-16/64 = 48/64 = 3/4

cos²x = 3/4

cos x = √3/4 = √3/2

cos 6x = 6 x √3/2 = 3√3

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.