Suppose cos θ=u in ^0<θ<(π)/(2) . Then tan θ= (A) 1 (B) (1)/(√(1-u^2)) (C) √(1-u^2) (D) √(1-u^2)

Name: Problem 49, Chapter 1: Math Level 2 SAT Subject Test
Uploaded: 2019-08-28T03:54:18-08:00
Duration: 2 min 1 s
Channel: Rikhil Makwana
Description: Suppose cos θ=u in ^0<θ<(π)/(2) . Then tan θ= (A) 1 (B) (1)/(√(1-u^2)) (C) √(1-u^2) (D) √(1-u^2) (E) (√(1-u^2))/(u)

step 1 Hello everybody, this is Ricky, and today we're working on problem 49 from the diagnostic. We're

Question

Suppose cos $\theta=u$ in $^{0<\theta<\frac{\pi}{2}}$ . Then tan $\theta=$ (A) 1 (B) $\frac{1}{\sqrt{1-u^{2}}}$ (C) $\sqrt{1-u^{2}}$ (D) $\sqrt{1-u^{2}}$ (E) $\frac{\sqrt{1-u^{2}}}{u}$

   Suppose cos $\theta=u$ in $^{0<\theta<\frac{\pi}{2}}$ . Then tan $\theta=$
(A) 1
(B) $\frac{1}{\sqrt{1-u^{2}}}$
(C) $\sqrt{1-u^{2}}$
(D) $\sqrt{1-u^{2}}$
(E) $\frac{\sqrt{1-u^{2}}}{u}$

Math Level 2 SAT Subject Test

Richard Ku, Howard… 10th Edition

Chapter 1, Problem 49

Instant Answer

Solved by Expert Rikhil Makwana

08/28/2019

Step 1

We also know that $\sin^2 \theta + \cos^2 \theta = 1$. So, we can find $\sin \theta$ using this identity: $\sin^2 \theta = 1 - \cos^2 \theta = 1 - u^2$ Taking the square root of both sides, we get: Show more…

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Suppose cos $\theta=u$ in $^{0<\theta<\frac{\pi}{2}}$ . Then tan $\theta=$ (A) 1 (B) $\frac{1}{\sqrt{1-u^{2}}}$ (C) $\sqrt{1-u^{2}}$ (D) $\sqrt{1-u^{2}}$ (E) $\frac{\sqrt{1-u^{2}}}{u}$

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Key Concepts

Pythagorean Identity

The Pythagorean identity, sin²? + cos²? = 1, is a fundamental relationship in trigonometry that connects the sine and cosine of an angle. When cos? is given as u, this identity allows us to solve for sin?, yielding sin? = ?(1 - u²) in the case of a positive sine value in the first quadrant.

Definition of Tangent

Tangent of an angle is defined as the ratio of the sine to the cosine, expressed as tan? = sin?/cos?. By substituting the value of sin? derived from the Pythagorean identity and recognizing cos? as u, we obtain tan? in terms of u.

First Quadrant Consideration

In the interval 0 < ? < ?/2, both sine and cosine are positive, which means that the square root operation will yield a positive result. This property assures that no ambiguity arises in the sign of sin? when applying the Pythagorean identity.

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