Advertisements
Advertisements
Question
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Advertisements
Solution
We know that cos2θ + sin2θ = 1
`cos^2theta + (- 2/3)^2` = 1
`cos^2theta + 4/9` = 1
cos2θ = `1 - 4/9`
cos2θ = `(9 - 4)/9 = 5/9`
cos θ = `+- sqrt(5)/3`
Since θ lies in the fourth quadrant cos θ is positive.
cos θ = `sqrt(5)/3`
sin θ = `- 2/3`, cosec θ = `1/sintheta = - 3/2`
cos θ = `sqrt(5)/3`, sec θ = `1/costheta = 3/sqrt(5)`
tan θ = `sintheta/costheta = (-2/3)/(sqrt(5)/3) = - 2/sqrt(5)`
cot θ = `1/tantheta = - sqrt(5)/2`
APPEARS IN
RELATED QUESTIONS
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
Prove that sin(π + θ) = − sin θ.
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Find the value of tan(α + β), given that cot α = `1/2`, α ∈ `(pi, (3pi)/2)` and sec β = `- 5/3` β ∈ `(pi/2, pi)`
Find the value of cos 2A, A lies in the first quadrant, when sin A = `4/5`
Express the following as a sum or difference
sin 4x cos 2x
Express the following as a sum or difference
2 sin 10θ cos 2θ
Express the following as a product
sin 50° + sin 40°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
If A + B + C = 180°, prove that `tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2` = 1
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
