Advertisements
Advertisements
प्रश्न
Find the value of the trigonometric functions for the following:
sec θ = `13/5`, θ lies in the IV quadrant
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the values of sin(480°)
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
Find all the angles between 0° and 360° which satisfy the equation sin2θ = `3/4`
If sin A = `3/5` and cos B = `9/41, 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of cos(A – B)
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`
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Show that tan(45° + A) = `(1 + tan"A")/(1 - tan"A")`
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)`
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = `("k" - 1)/("k" + 1)` sin α
If θ is an acute angle, then find `cos (pi/4 + theta/2)`, when sin θ = `8/9`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Show that `(sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x)` = tan 2x
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
