Advertisements
Advertisements
प्रश्न
If sin A = `3/4`, calculate cos A and tan A.
Advertisements
उत्तर
Let ΔABC be a right-angled triangle, right-angled at point B.
Given that,
sin A = `3/4`
`("BC")/("AC") = 3/4`
Let BC be 3k.
Therefore, AC will be 4k, where k is a positive integer.
Applying Pythagoras theorem in ΔABC, we obtain
AC2 = AB2 + BC2
(4k)2 = AB2 + (3k)2
16k2 − 9k2 = AB2
7k2 = AB2
AB = `sqrt7k`
cos A = `("Side adjacent to ∠A")/"Hypotenuse"`
∴ cos A = `("AB")/("AC")`
= `sqrt(7k)/(4k)`
= `sqrt7/4`
tan A = `("Side adjacent to ∠A")/("Side adjacent to ∠A")`
= `("BC")/("AB")`
= `(3k)/(sqrt7k)`
= `3/sqrt7`
APPEARS IN
संबंधित प्रश्न
If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
If `tan theta = 1/sqrt7` `(cosec^2 theta - sec^2 theta)/(cosec^2 theta + sec^2 theta) = 3/4`
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
Evaluate the Following
`cot^2 30^@ - 2 cos^2 60^circ- 3/4 sec^2 45^@ - 4 sec^2 30^@`
Find the value of x in the following :
`2 sin x/2 = 1`
Find the value of x in each of the following :
cos x = cos 60º cos 30º + sin 60º sin 30º
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If sin 2A = `1/2` tan² 45° where A is an acute angle, then the value of A is ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
Find the value of sin 0° + cos 0° + tan 0° + sec 0°.
Prove that: cot θ + tan θ = cosec θ·sec θ
Proof: L.H.S. = cot θ + tan θ
= `square/square + square/square` ......`[∵ cot θ = square/square, tan θ = square/square]`
= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
= `1/square xx 1/square`
= cosec θ·sec θ ......`[∵ "cosec" θ = 1/square, sec θ = 1/square]`
= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
If θ is an acute angle and sin θ = cos θ, find the value of tan2 θ + cot2 θ – 2.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
In ΔBC, right angled at C, if tan A = `8/7`, then the value of cot B is ______.
Evaluate: 5 cosec2 45° – 3 sin2 90° + 5 cos 0°.
