Advertisements
Advertisements
प्रश्न
Find the value of the trigonometric functions for the following:
cos θ = `2/3`, θ lies in the I quadrant
Advertisements
उत्तर
We know that cos2θ + sin2θ = 1
`(2/3)^2 + sin^2theta` = 1
`4/9 + sin^2theta` = 1
sin2θ = `1 - 4/9`
sin2θ = `(9 - 4)/9 = 5/9`
sin θ = `+- sqrt(5)/3`
Since θ lies in the I quadrant all trigonometric functions are positive.
sin θ = `sqrt(5)/3`, cosec θ = `1/sintheta = 3/sqrt(5)`
cos θ = `2/3`, sec θ = `1/costheta = 3/2`
tan θ = `sintheta/costheta = (sqrt(5)/3)/(2/3) = sqrt(5)/2`
cot θ = `costheta/sintheta = (2/3)/(sqrt(5)/3) = 2/sqrt(5)`
APPEARS IN
संबंधित प्रश्न
Find the values of tan(1050°)
Find the values of cot(660°)
Find the values of `tan ((19pi)/3)`
`(5/7, (2sqrt(6))/7)` is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Find the value of the trigonometric functions for the following:
cos θ = `- 2/3`, θ lies in the IV quadrant
If sin A = `3/5` and cos B = `9/41 0 < "A" < pi/2, 0 < "B" < pi/2`, find the value of sin(A + B)
Find the value of sin105°.
Show that tan 75° + cot 75° = 4
Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`
Find the value of cos 2A, A lies in the first quadrant, when cos A = `15/17`
If cos θ = `1/2 ("a" + 1/"a")`, show that cos 3θ = `1/2 ("a"^3 + 1/"a"^3)`
Express the following as a sum or difference
sin 35° cos 28°
Express the following as a product
sin 50° + sin 40°
Show that sin 12° sin 48° sin 54° = `1/8`
Show that `((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta))` = 1
If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos "A"/2 cos "B"/2 sin "C"/2`
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`
