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
In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:
sin C, cos C
State whether the following are true or false. Justify your answer.
The value of tan A is always less than 1.
If 4 tan θ = 3, evaluate `((4sin theta - cos theta + 1)/(4sin theta + cos theta - 1))`
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin A = 2/3`
If `sin theta = a/b` find sec θ + tan θ in terms of a and b.
If `tan θ = 20/21` show that `(1 - sin theta + cos theta)/(1 + sin theta + cos theta) = 3/7`
Evaluate the Following
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°
Evaluate the Following
`(sin 30^@ - sin 90^2 + 2 cos 0^@)/(tan 30^@ tan 60^@)`
Find the value of x in the following :
`sqrt3 tan 2x = cos 60^@ + sin45^@ cos 45^@`
Find the value of x in the following :
cos 2x = cos 60° cos 30° + sin 60° sin 30°
If sin (A − B) = sin A cos B − cos A sin B and cos (A − B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
The value of sin² 30° – cos² 30° is ______.
The value of cos 0°. cos 1°. cos 2°. cos 3°… cos 89° cos 90° is ______.
Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.
If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.
The maximum value of the expression 5cosα + 12sinα – 8 is equal to ______.
If `θ∈[(5π)/2, 3π]` and 2cosθ + sinθ = 1, then the value of 7cosθ + 6sinθ is ______.
Evaluate 2 sec2 θ + 3 cosec2 θ – 2 sin θ cos θ if θ = 45°.
