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Chapter 7: Q.9 (page 473)

Rewrite in terms of sine and cosine functions: $\tan (θ) c s c (θ)$

Short Answer

Expert verified

In terms of sine and cosine function we get,

$\frac{1}{\cos θ}$

Step by step solution

01

Given information

We are given an trigonometric function as $\tan (θ) c sc (θ)$

02

We use trigonometric formulastan(θ)=sinθcosθcscθ=1sinθ

We get,

$\tan (θ) c sc (θ) = \frac{\sin (θ)}{\cos (θ)} \frac{1}{\sin (θ)} = \frac{1}{\cos (θ)} = s e c θ$

03

Conclusion

The function in terms of sine and cosine can be given as $\frac{1}{\cos θ}$

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Most popular questions from this chapter

(a) $\sin \frac{π}{4} \cdot \cos \frac{π}{3} =______$

(b) $\tan \frac{π}{4} - \sin \frac{π}{6} =________$

Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. A first approximation to the sawtooth curve is given by

$y = \frac{1}{2} \sin (2 π x) + \frac{1}{4} \sin (4 π x)$

Show that $y = \sin (2 π x) \cos^{2} (π x)$

Express the product $\cos 3 θ \cos 5 θ$ as a sum containing only sines or only cosines.

If $\tan θ = a \tan \frac{θ}{3}$ , express $\tan \frac{θ}{3}$ in terms of a.

Establish each identity.

$\frac{1}{1 - \sin θ} + \frac{1}{1 + \sin θ} = 2 s e c^{2} θ$

See all solutions

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