Advertisements
Advertisements
Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
Advertisements
Solution
We know that `tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 8/15`
Now consider a right-angled Δle ABC.
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
๐ฅ2 = 82 + 152
๐ฅ2 = 225 + 64 = 289
`x = sqrt289 = 17`
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 8/17`
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 15/17`
`tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 8/15`
`cot theta = 1/tan theta = 1/(8/15) = 15/8`
`cosec theta = 1/sin theta = (1/8)/17 = 17/8`
`sec theta = 1/cos theta= (1/15)/17 = 17/15`
APPEARS IN
RELATED QUESTIONS
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of
- sin A cos C + cos A sin C
- cos A cos C − sin A sin C
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If 3 cot θ = 2, find the value of `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
If sin θ = `12/13`, Find `(sin^2 θ - cos^2 θ)/(2sin θ cos θ) × 1/(tan^2 θ)`.
if `sec A = 17/8` verify that `(3 - 4sin^2A)/(4 cos^2 A - 3) = (3 - tan^2 A)/(1 - 3 tan^2 A)`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
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 sin A = `1/2`, then the value of cot A is ______.
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) 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))`
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
