Advertisements
Advertisements
Question
Find the principal values of the following:
`cos^-1(-sqrt3/2)`
Advertisements
Solution
Let `cos^-1(-sqrt3/2) = y`
Then,
`cosy=-sqrt3/2`
We know that the range of the principal value branch is [0, π].
Thus,
`cosy=-sqrt3/2=cos((5pi)/6)`
`=>y=(5pi)/6in[0,pi]`
Hence, the principal value of `cos^-1(-sqrt3/2)` is `(5pi)/6.`
APPEARS IN
RELATED QUESTIONS
If (tan−1x)2 + (cot−1x)2 = 5π2/8, then find x.
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
`sin^-1(sin pi/6)`
`sin^-1(sin (5pi)/6)`
`sin^-1(sin12)`
Evaluate the following:
`cos^-1(cos3)`
Evaluate the following:
`cos^-1(cos12)`
Evaluate the following:
`tan^-1(tan1)`
Evaluate the following:
`cot^-1(cot pi/3)`
Evaluate the following:
`cot^-1(cot (4pi)/3)`
Evaluate the following:
`cot^-1{cot ((21pi)/4)}`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`
Write the following in the simplest form:
`tan^-1{(sqrt(1+x^2)+1)/x},x !=0`
Write the following in the simplest form:
`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`
Evaluate the following:
`sin(sec^-1 17/8)`
Evaluate the following:
`sec(sin^-1 12/13)`
Evaluate:
`sec{cot^-1(-5/12)}`
Evaluate:
`sin(tan^-1x+tan^-1 1/x)` for x > 0
`sin^-1x=pi/6+cos^-1x`
Solve the following equation for x:
`tan^-1 (x-2)/(x-1)+tan^-1 (x+2)/(x+1)=pi/4`
`sin^-1 5/13+cos^-1 3/5=tan^-1 63/16`
`(9pi)/8-9/4sin^-1 1/3=9/4sin^-1 (2sqrt2)/3`
Prove that:
`2sin^-1 3/5=tan^-1 24/7`
Solve the following equation for x:
`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`
Write the value of `sin^-1((-sqrt3)/2)+cos^-1((-1)/2)`
Write the value of cos\[\left( 2 \sin^{- 1} \frac{1}{3} \right)\]
Write the value of cos−1 (cos 6).
Write the value of tan−1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]
Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]
Write the value of \[\sin^{- 1} \left( \sin\frac{3\pi}{5} \right)\]
Write the value of \[\sec^{- 1} \left( \frac{1}{2} \right)\]
Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]
Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]
The value of \[\sin\left( 2\left( \tan^{- 1} 0 . 75 \right) \right)\] is equal to
If x > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find \[\frac{dy}{dx}\] When \[\theta = \frac{\pi}{3}\] .
Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ; 1 < x < 1\].
Find the value of x, if tan `[sec^(-1) (1/x) ] = sin ( tan^(-1) 2) , x > 0 `.
The value of sin `["cos"^-1 (7/25)]` is ____________.
