Advertisements
Advertisements
рдкреНрд░рд╢реНрди
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cos theta = 12/2`
Advertisements
рдЙрддреНрддрд░
`cos theta = "ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ"/"тДОЁЭСжЁЭСЭЁЭСЬЁЭСбЁЭСТЁЭСЫЁЭСвЁЭСаЁЭСТ" = 12/15`
Let x be the opposite side.
By applying Pythagoras theorem
ЁЭР┤ЁЭР╢2 = ЁЭР┤ЁЭР╡2 + ЁЭР╡ЁЭР╢2
225 = ЁЭСе2 + 144
225 − 144 = ЁЭСе2
ЁЭСе2 = 81
ЁЭСе = 9
`sin theta = "ЁЭСЬЁЭСЭЁЭСЭЁЭСЬЁЭСаЁЭСЦЁЭСбЁЭСТ ЁЭСаЁЭСЦЁЭССЁЭСТ"/"тДОЁЭСжЁЭСЭЁЭСЬЁЭСбЁЭСТЁЭСЫЁЭСвЁЭСаЁЭСТ" = 9/15`
`tan theta = "ЁЭСЬЁЭСЭЁЭСЭЁЭСЬЁЭСаЁЭСЦЁЭСбЁЭСТ ЁЭСаЁЭСЦЁЭССЁЭСТ"/"ЁЭСОЁЭССЁЭСЧЁЭСОЁЭСРЁЭСТЁЭСЫЁЭСб ЁЭСаЁЭСЦЁЭССЁЭСТ" = 9/12`
`cosec theta = 1/sin theta = (1/9)/15 = 15/9`
`sec theta = 1/cos theta = (1/12)/15 = 15/12`
`cot theta = 1/tan theta = (1/9)/12 = 12/9`
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sec theta = 13/5`
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 `sec θ = 13/5`, show that `(2 sin θ - 3 cos θ)/(4 sin θ - 9 cos θ) = 3`.
If sin θ = `12/13`, Find `(sin^2 θ - cos^2 θ)/(2sin θ cos θ) × 1/(tan^2 θ)`.
if `tan theta = 12/13` Find `(2 sin theta cos theta)/(cos^2 theta - sin^2 theta)`
Evaluate the following
`2 sin^2 30^2 - 3 cos^2 45^2 + tan^2 60^@`
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
Evaluate the Following
`sin 30^2/sin 45^@ + tan 45^@/sec 60^@ - sin 60^@/cot 45^@ - cos 30^@/sin 90^@`
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
sin (45° + θ) – cos (45° – θ) is equal to ______.
If `sqrt2 sin (60° – α) = 1` then α is ______.
If x sin (90° – θ) cot (90° – θ) = cos (90° – θ), then x is equal to ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Prove that sec θ + tan θ = `cos θ/(1 - sin θ)`.
Proof: L.H.S. = sec θ + tan θ
= `1/square + square/square`
= `square/square` ......`(тИ╡ sec θ = 1/square, tan θ = square/square)`
= `((1 + sin θ) square)/(cos θ square)` ......[Multiplying `square` with the numerator and denominator]
= `(1^2 - square)/(cos θ square)`
= `square/(cos θ square)`
= `cos θ/(1 - sin θ)` = R.H.S.
∴ L.H.S. = R.H.S.
∴ sec θ + tan θ = `cos θ/(1 - sin θ)`
What will be the value of sin 45° + `1/sqrt(2)`?
If cos(α + β) = `(3/5)`, sin(α – β) = `5/13` and 0 < α, β < `π/4`, then tan (2α) is equal to ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
