If cos-0-6- find 5 sin-3 tan-a 0-4b 0-2c 0-3d 0

(d) 0 We have: cos θ = 610=35 ⇒ ABAC=35=3k5k BC2 = (AC2 AB2) = (25k2 9k2) = 16k2 BC=16k2=4k ∴ sin θ = BCAC=4k5k=45, nbsp; tan θ = BCAB=4k3k=43 Hence, 5 s ...

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Standard X

Mathematics

Relation between Trigonometric Ratios

If cosθ=0.6, ...

Question

If cos θ = 0.6, find 5 sin θ − 3 tan θ.
(a) 0.4
(b) 0.2
(c) 0.3
(d) 0

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Solution

(d) 0
We have:
cos θ = $\frac{6}{10} = \frac{3}{5}$
⇒ $\frac{A B}{A C} = \frac{3}{5} = \frac{3 k}{5 k}$

BC² = (AC² - AB²)
= (25k² - 9k²)
= 16k²
$B C = \sqrt{16 k^{2}} = 4 k$
∴ sin θ = $\frac{B C}{A C} = \frac{4 k}{5 k} = \frac{4}{5}$ , tan θ = $\frac{B C}{A B} = \frac{4 k}{3 k} = \frac{4}{3}$
Hence,
5 sin θ − 3 tan θ
$= 5 \times \frac{4}{5} - 3 \times \frac{4}{3} = 4 - 4 = 0$

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If cos θ = 0.6, find 5 sin θ − 3 tan θ. (a) 0.4 (b) 0.2 (c) 0.3 (d) 0

(d) 0 We have: cos θ = 610=35 ⇒ ABAC=35=3k5k BC2 = (AC2 - AB2) = (25k2 - 9k2) = 16k2 BC=16k2=4k ∴ sin θ = BCAC=4k5k=45, tan θ = BCAB=4k3k=43 Hence, 5 sin θ − 3 tan θ =5×45-3×43=4-4=0

If cos θ = 0.6, find 5 sin θ − 3 tan θ.
(a) 0.4
(b) 0.2
(c) 0.3
(d) 0