Question

Describe how you can determine the sign (positive or negative) of the cosine, sine, and tangent of a particular angle without using technology (using your calculator). Explain using primary trigonometric ratios. Use q = 170° to illustrate your process.

a) Cosine is positive, sine is positive, tangent is negative.

b) Cosine is negative, sine is positive, tangent is negative.

c) Cosine is negative, sine is negative, tangent is positive.

d) Cosine is positive, sine is negative, tangent is positive.

Answer 1

To determine the sign of trigonometric functions, consider an angle's position within a unit circle's quadrants. For 170°, it's in the second quadrant where cosine is negative, sine is positive, and tangent is negative.

Step-by-step explanation:

To determine the sign of the cosine, sine, and tangent of a particular angle without technology, you can first consider the angle's location within the unit circle divided into four quadrants. Each quadrant corresponds to a specific combination of signs for these trigonometric functions based on the x and y values in the coordinate plane (with the x-axis being the cos value and the y-axis being the sin value).

For the angle q = 170°, it lies in the second quadrant where cosine is negative (due to the x values being negative here) and sine is positive (since y values are positive). The tangent, which is the ratio of sine to cosine, would be negative here given that we have a positive value divided by a negative one.

Solution for q = 170°

• Cosine is negative because x values in quadrant II are negative.
• Sine is positive because y values in quadrant II are positive.
• Tangent is negative because it is the ratio of sine over cosine and these have opposite signs in quadrant II.

Therefore, the correct answer for q = 170° is:

(b) Cosine is negative, sine is positive, tangent is negative.