Advertisements
Advertisements
प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Advertisements
उत्तर
We know sin2θ + cos2θ = 1
`sin^2theta + (-1/2)^2` = 1
`sin^2theta + 1/4` = 1
sin2θ = `1 - 1/4 = 3/4`
sin θ = `+- sqrt(3)/2`
sin θ = `- sqrt(3)/2`,
cosec θ = `- 2/sqrt(3)`
tan θ = `sintheta/costheta = (-sqrt(3)/2)/(- 1/2) = sqrt(3)`
cot θ = `1/tantheta = 1/sqrt(3)`
sec θ = `1/costheta = 1/(-1/2)` = – 2
APPEARS IN
संबंधित प्रश्न
Find the values of sin(480°)
Find the values of cos(300°)
Find the values of `sin (-(11pi)/3)`
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Find cos(x − y), given that cos x = `- 4/5` with `pi < x < (3pi)/2` and sin y = `- 24/25` with `pi < y < (3pi)/2`
Find sin(x – y), given that sin x = `8/17` with 0 < x < `pi/2`, and cos y = `- 24/25`, x < y < `(3pi)/2`
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = `pi/2`
Show that tan 75° + cot 75° = 4
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
If tan x = `"n"/("n" + 1)` and tan y = `1/(2"n" + 1)`, find tan(x + y)
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
Find the value of cos 2A, A lies in the first quadrant, when tan A `16/63`
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos "B"/2 sin "C"/2`
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
