If sin Θ = 2 over 3 and tan Θ < 0, what is the value of cos Θ?

Mathematics

2 answers:

guapka [62]3 years ago

6 0

If sin Θ is positive and tan Θ is negative, then the angle should be in the second quadrant using the rule of thumb. In this case, cos Θ is expected to be negative. Using the calculator, the answer is -0.7454. This is equivalent to option D. <span>negative square root of 5 over 3</span>

RideAnS [48]3 years ago

6 0

If sin Θ = 2 over 3 and tan Θ < 0, then the value of cos Θ = - (√5) / 3

<h3>Further explanation</h3>

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

<h3>sin ∠A = opposite / hypotenuse</h3><h3>cos ∠A = adjacent / hypotenuse</h3><h3>tan ∠A = opposite / adjacent </h3>

Let us now tackle the problem!

If $\sin \theta = 2 / 3$ , then :

$\text{opposite = 2}$

$\text{hypotenuse = 3}$

We can calculate adjacent by using Pythagorean theorem .

$adjacent^2 = hypotenuse^2 - opposite^2$

$adjacent^2 = 3^2 - 2^2$

$adjacent^2 = 9 - 4$

$adjacent^2 = 5$

$adjacent = \sqrt{5}$

Finally we can calculate the value of cos Θ in the following way :

$\cos \theta = -\text{adjacent / hypotenuse}$

$\large {\boxed {\cos \theta = \frac{-\sqrt{5}}{3}} } }$

We give a negative sign because tan Θ < 0, and this means the angle is between 90° and 180°

<h3>Learn more</h3>

Calculate Angle in Triangle : brainly.com/question/12438587
Periodic Functions and Trigonometry : brainly.com/question/9718382
Trigonometry Formula : brainly.com/question/12668178

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse

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Look at the figure if tan x=3/y and cos x =y/z what is the value of sin x?

castortr0y [4]

Recall:

The tan of the measure of an angle is the ratio of the opposite side to the adjacent side to that angle, that is :

$\displaystyle{ \tan x^{\circ}= \frac{opposite\ side}{adjacent \ side}$ .

Since this ratio is 3/y, we denote the opposite side, and adjacent side respectively by 3 and y.

(Technically we should write 3t and yt, but we try our luck as we see y in the second ratio too!)

Similarly, $\displaystyle{\cos x^{\circ}= \frac{adjacent\ side}{hypothenuse}$ .

The adjacent side is already denoted by y, so we denote the length of the hypotenuse by z.

Now the sides of the right triangle are complete.

$\displaystyle{ \sin x^{\circ}= \frac{opposite\ side}{hypotenuse}= \frac{3}{z}$

Answer: A