Advertisements
Advertisements
Question
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Advertisements
Solution
`cos theta = 5/13`
`sin^2 theta = 1 - cos^2 theta = 1 - 25/169 = 144/169`
`sin theta = +- 12/13` as `theta` is acute, therefore `sintheta` must be positive
`:. sin theta = 12/13`
APPEARS IN
RELATED QUESTIONS
If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p
The angles of depression of two ships A and B as observed from the top of a light house 60 m high are 60° and 45° respectively. If the two ships are on the opposite sides of the light house, find the distance between the two ships. Give your answer correct to the nearest whole number.
Prove the following trigonometric identities:
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Prove the following identities:
`(sinAtanA)/(1 - cosA) = 1 + secA`
Prove the following identities:
`1/(cosA + sinA) + 1/(cosA - sinA) = (2cosA)/(2cos^2A - 1)`
`sqrt((1 + sin θ)/(1 - sin θ)) = sec θ + tan θ`

From the figure find the value of sinθ.
If \[sec\theta + tan\theta = x\] then \[tan\theta =\]
If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ =
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`
Prove the following identity :
`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`
Without using trigonometric table , evaluate :
`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`
If x = a sec θ + b tan θ and y = a tan θ + b sec θ prove that x2 - y2 = a2 - b2.
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove that cosec θ – cot θ = `(sin θ)/(1 + cos θ)`.
If 4 tanβ = 3, then `(4sinbeta-3cosbeta)/(4sinbeta+3cosbeta)=` ______.
sec θ when expressed in term of cot θ, is equal to ______.
