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
`(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:
tan θ = −2, θ lies in the II quadrant
Show that `sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9` = 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`
Find the value of cos 105°.
If x cos θ = `y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3)`. find the value of xy + yz + zx
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° − A) = `(1 - tan "A")/(1 + tan "A")`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Prove that `tan (pi/4 + theta) - tan(pi/4 - theta)` = 2 tan 2θ
Show that `cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)`
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
cos 35° – cos 75°
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 `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
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 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 cos2 B + cos2 C = 1
