Advertisements
Advertisements
Question
If cosθ = `5/13`, then find sinθ.
Advertisements
Solution
cosθ = `5/13`
`sin^2θ + cos^2θ = 1`
`sin^2θ + (5/13)^2 = 1`
`sin^2θ = (1 - 25)/169`
`sin^2θ = (169 - 25)/169`
`sin^2θ = 144/169`
sinθ = `sqrt(144/169)`
sinθ = `12/13`
APPEARS IN
RELATED QUESTIONS
If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`
Express the ratios cos A, tan A and sec A in terms of sin A.
9 sec2 A − 9 tan2 A = ______.
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following identities:
`(1 + sinA)/cosA + cosA/(1 + sinA) = 2secA`
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Prove that:
(sec A − tan A)2 (1 + sin A) = (1 − sin A)
`(1-cos^2theta) sec^2 theta = tan^2 theta`
`cot theta/((cosec theta + 1) )+ ((cosec theta +1 ))/ cot theta = 2 sec theta `
Prove the following identities:
`(cot^2 theta (sec theta - 1))/((1 + sin theta)) + (sec^2 theta(sin theta - 1))/((1 + sec theta)) = 0`
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, prove that (m2 + n2) = (a2 + b2).
From the figure find the value of sinθ.
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove the following identity :
`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`
If sin θ = `1/2`, then find the value of θ.
A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/min.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that cot2θ × sec2θ = cot2θ + 1.
Prove that `(cot A)/(1 - cot A) + (tan A)/(1 - tan A) = -1`.
If tan θ + sec θ = l, then prove that sec θ = `(l^2 + 1)/(2l)`.
