Advertisements
Advertisements
Question
Find the value of the trigonometric functions for the following:
cos θ = `- 1/2`, θ lies in the III quadrant
Advertisements
Solution
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
RELATED QUESTIONS
Find the values of cos(300°)
Find the values of tan(1050°)
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Prove that `(cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta))` = cos2θ cotθ
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)
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 sin(A + B) sin(A – B) = sin2A – sin2B
If cos(α – β) + cos(β – γ) + cos(γ – α) = `- 3/2`, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
If θ is an acute angle, then find `sin (pi/4 - theta/2)`, when sin θ = `1/25`
Express the following as a sum or difference
sin 4x cos 2x
Prove that `(sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x)` = tan 4x
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
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 sin2 B + sin2 C = 1
Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
