If sin Θ = 2 over 3 and tan Θ < 0, then the value of cos Θ = - (√5) / 3
Further explanation
Firstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenuse
cos ∠A = adjacent / hypotenuse
tan ∠A = opposite / adjacent
Let us now tackle the problem!
If [tex]\sin \theta = 2 / 3[/tex] , then :
[tex]\text{opposite = 2}[/tex]
[tex]\text{hypotenuse = 3}[/tex]
We can calculate adjacent by using Pythagorean theorem .
[tex]adjacent^2 = hypotenuse^2 - opposite^2[/tex]
[tex]adjacent^2 = 3^2 - 2^2[/tex]
[tex]adjacent^2 = 9 - 4[/tex]
[tex]adjacent^2 = 5[/tex]
[tex]adjacent = \sqrt{5}[/tex]
Finally we can calculate the value of cos Θ in the following way :
[tex]\cos \theta = -\text{adjacent / hypotenuse}[/tex]
[tex]\large {\boxed {\cos \theta = \frac{-\sqrt{5}}{3}} } }[/tex]
We give a negative sign because tan Θ < 0, and this means the angle is between 90° and 180°
Learn more
- Calculate Angle in Triangle : https://brainly.com/question/12438587
- Periodic Functions and Trigonometry : https://brainly.com/question/9718382
- Trigonometry Formula : https://brainly.com/question/12668178
Answer details
Grade: High School
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse
