Advertisements
Advertisements
प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of cos(x − y)
If sin x = `15/17` and cos y = `12/13, 0 < x < pi/2, 0 < y < pi/2`, find the value of tan(x + y)
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
Prove that `tan(pi/4 + theta) tan((3pi)/4 + theta)` = – 1
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`
Prove that sin 4α = `4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2`
Prove that `32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6` = 3
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a product
cos 35° – cos 75°
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Prove that `sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2` = sin 2θ sin 5θ
Show that cot(A + 15°) – tan(A – 15°) = `(4cos2"A")/(1 + 2 sin2"A")`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
