Question

Find one positive angle whose sine is negative 0.70.

Answer 1

Answer:

• Both 2.34 radians and 5.48 radians (approximately) are positive angles whose sine is - 0.70

Explanation:

The sine is the y-coordinate of the point on the unit circle.

The graph shows that, in the first quadrant, the point with y-coordinate = 0.7 has an angle of 0.8 radians (you read it by moving horizontally to the right from the y-axis at the height of 0.70).

Hence, the sine of 0.8 radians is 0.70 (positive).

The sine is negative in the third and fourth quadrants (the y-coordinate is negative below the y-axis).

Then, 0.8 radians is your reference angle.

• The positive angle in the third quadrant is π radians - reference angle. This is, π radians - 0.8 radians ≈ 3.14 radians - 0.8 radians = 2.34 radians.

• The positive angle in the fourth quadrant if 2π radians - 0.8 radians ≈ 6.28 radians - 0.8 radians = 5.48 radians.