Advertisements
Advertisements
Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
Advertisements
Solution
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 12/15`
Let x be the opposite side.
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
225 = ๐ฅ2 + 144
225 − 144 = ๐ฅ2
๐ฅ2 = 81
๐ฅ = 9
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 9/15`
`tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 9/12`
`cosec theta = 1/sin theta = (1/9)/15 = 15/9`
`sec theta = 1/cos theta = (1/12)/15 = 15/12`
`cot theta = 1/tan theta = (1/9)/12 = 12/9`
APPEARS IN
RELATED QUESTIONS
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin A, cos A
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
Find the value of x in the following :
`2 sin x/2 = 1`
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
sin (45° + θ) – cos (45° – θ) is equal to ______.
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
Prove the following:
If tan A = `3/4`, then sinA cosA = `12/25`
The value of the expression (sin 80° – cos 80°) is negative.
In the given figure, if sin θ = `7/13`, which angle will be θ?
Find an acute angle θ when `(cos θ - sin θ)/(cos θ + sin θ) = (1 - sqrt(3))/(1 + sqrt(3))`
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
