Advertisements
Advertisements
рдкреНрд░рд╢реНрди
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
Advertisements
рдЙрддреНрддрд░
`cot alpha = "ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ"/"ЁЭСЬЁЭСЭЁЭСЭЁЭСЬЁЭСаЁЭСЦЁЭСбЁЭСТ ЁЭСаЁЭСЦЁЭССЁЭСТ" = 12/5`
Now consider a right-angled Δle ABC,
By applying Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
ЁЭСе2 = 25 + 144
`x^2 = 169 = sqrt169`
ЁЭСе = 13
`tan theta = 1/cot theta = (1/12)/5 = 5/12`
`sin theta = "ЁЭСЬЁЭСЭЁЭСЭЁЭСЬЁЭСаЁЭСЦЁЭСбЁЭСТ ЁЭСаЁЭСЦЁЭССЁЭСТ"/"тДОЁЭСжЁЭСЭЁЭСЬЁЭСбЁЭСТЁЭСЫЁЭСвЁЭСаЁЭСТ" = 5/13`
`cos theta = "ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ"/"тДОЁЭСжЁЭСЭЁЭСЬЁЭСбЁЭСТЁЭСЫЁЭСвЁЭСаЁЭСТ" = 12/13`
`cosec theta = 1/sin theta = 1/(5/13) = 13/5`
`sec theta = 1/cos theta = 1/(12/13) = 13/12`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
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`
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 `tan theta = 24/7`, find that sin ЁЭЬГ + cos ЁЭЬГ
If Cosec A = 2 find `1/(tan A) + (sin A)/(1 + cos A)`
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
Evaluate the Following
(cos 0° + sin 45° + sin 30°)(sin 90° − cos 45° + cos 60°)
Evaluate the Following:
`tan 45^@/(cosec 30^@) + sec 60^@/cot 45^@ - (5 sin 90^@)/(2 cos 0^@)`
If `sqrt2 sin (60° – α) = 1` then α is ______.
If cos (40° + A) = sin 30°, then value of A is ______.
If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
In ΔABC, ∠ABC = 90° and ∠ACB = θ. Then write the ratios of sin θ and tan θ from the figure.
Find the value of sin 45° + cos 45° + tan 45°.
If sin θ + cos θ = `sqrt(2)` then tan θ + cot 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 ______.
If sinθ = `1/sqrt(2)` and `π/2 < θ < π`. Then the value of `(sinθ + cosθ)/tanθ` is ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
In a right triangle PQR, right angled at Q. If tan P = `sqrt(3)`, then evaluate 2 sin P cos P.
