Advertisements
Advertisements
Question
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Solution
We know that sec2θ – tan2θ = 1
`(13/2)^2 - tan^2theta` = 1
`169/25 - 1` = tan2θ
tan2θ = `(169 - 25)/25 = 144/25`
tan θ = `+- 12/5`
Since θ lies in the fourth quadrant tan θ is negative.
∴ tan θ = `- 12/5`
cos θ = `1/sectheta = 5/13`
We know sin2θ + cos2θ = 1
`sin^2theta + (5/13)^2` = 1
sin2θ = `1 - 25/169`
sin2θ = `(169 - 25)/169 = 144/169`
sin θ = `+- 12/13`
Since θ lies in the fourth quadrant sin θ is negative.
∴ sin θ = `- 12/13`
sin θ = `- 12/13`, cosec θ = `1/sintheta = - 13/12`
cos θ = `5/13`, sec θ = `1/costheta = 13/5`
tan θ = `- 12/5`, cot θ = `1/tantheta = - 5/12`
APPEARS IN
RELATED QUESTIONS
Find the values of cos(300°)
Find the values of cot(660°)
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II 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 the value of sin 105°
Prove that cos(30° + x) = `(sqrt(3) cos x - sin x)/2`
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Express the following as a sum or difference
cos 5θ cos 2θ
Express the following as a product
sin 50° + sin 40°
Express the following as a product
cos 35° – cos 75°
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = `cos 2"A" + 1/4`
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 = 180°, prove that sin A + sin B + sin C = `4 cos "A"/2 cos "B"/2 cos "C"/2`
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
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`
