Advertisements
Advertisements
Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
Solution
consider a right-angled Δle ABC, we get
Let x be the adjacent side.
By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
`(sqrt10)^2 = 1^2 + x^2`
x2 = 10 − 1 = 9
x = 3
`sin theta = 1/cosec theta = 1/sqrt10`
`cos theta = "adjacent"/"hypotenuse" = 3/sqrt10`
`tan theta = "opposite sides"/"adjacebt side" = 1/3`
`sec theta = 1/cos theta = sqrt10/3`
`cot theta = 1/tan theta = (1/1)/3 = 3`
APPEARS IN
RELATED QUESTIONS
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
If tan θ = `a/b` prove that `(a sin theta - b cos theta)/(a sin theta + b cos theta) = (a^2 - b^2)/(a^2 + b^2)`
If `cot theta = 1/sqrt3` show that `(1 - cos^2 theta)/(2 - sin^2 theta) = 3/5`
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
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°.
If cos A + cos² A = 1, then sin² A + sin4 A is equal to ______.
What will be the value of sin 45° + `1/sqrt(2)`?
