We can start by drawing a reference triangle in quadrant 3, where cos(x) is negative and equal to -√2/3. This will be a 30-60-90 triangle with hypotenuse 1 and opposite side √3/2.
The adjacent side is negative since cos(x) is negative, so we have:
cos(x) = -√2/3 = adjacent/hypotenuse = -1/√3
multiplying both sides by -√3, we get:
-√2 = adjacent
And:
sin(x) = opposite/hypotenuse = √3/2
tan(x) = opposite/adjacent = -√3/2
csc(x) = 1/sin(x) = 2/√3
sec(x) = 1/cos(x) = -√3/2
cot(x) = 1/tan(x) = -2/√3
cosx=-root2/3 and x is in quadrant 3
Use identities to find the exact values at x for the remaining five trigonometric functions
1 answer