The exact value of sin(v + w) for the given values of sin (v) and cos (w) is 0.37.
What is the sine and cosine of an angle in a right triangle?
The sine of an angle is the ratio of the height to the hypotenuse of the given triangle.
The cosine of the angle is the ratio of the base to the hypotenuse of the triangle.
Given, sin (v) = - 3/5, cos (w) = 10/11
Therefore, cos (v) = √[1 - (- 3/5)²] = √[1 - 9/25] = √(16/25) = - 4/5 (As, 'v' is an angle in Quadrant III)
sin (w) = √[1 - (10/11)²] = √[1 - 100/121] = √(21/100) = - (√21)/10 (As, 'w' is an angle in Quadrant IV)
Now, sin(v + w)
= sin (v) cos (w) + cos (v)sin (w)
= (- 3/5)(10/11) + (- 4/5)(- √21)/10
= -6/11 + (2√21)/10
= - 0.55 + 0.92
= 0.37
Learn more about the sine and cosine of an angle here: https://brainly.com/question/21182511
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