Advertisements
Advertisements
Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
Advertisements
Solution
`cot alpha = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐" = 12/5`
Now consider a right-angled Δle ABC,
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
๐ฅ2 = 25 + 144
`x^2 = 169 = sqrt169`
๐ฅ = 13
`tan theta = 1/cot theta = (1/12)/5 = 5/12`
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 5/13`
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 12/13`
`cosec theta = 1/sin theta = 1/(5/13) = 13/5`
`sec theta = 1/cos theta = 1/(12/13) = 13/12`
APPEARS IN
RELATED QUESTIONS
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
State whether the following are true or false. Justify your answer.
cos A is the abbreviation used for the cosecant of angle A.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin A = 2/3`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
tan θ = 11
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
if `sin theta = 3/4` prove that `sqrt(cosec^2 theta - cot)/(sec^2 theta - 1) = sqrt7/3`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the following:
(cosec2 45° sec2 30°)(sin2 30° + 4 cot2 45° − sec2 60°)
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.
If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.
If sin θ + sin² θ = 1, then cos² θ + cos4 θ = ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Let f(x) = sinx.cos3x and g(x) = cosx.sin3x, then the value of `7((f(π/7) + g(π/7))/(g((5π)/14) + f((5π)/14)))` is ______.
