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il63 [147K]
3 years ago
12

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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