(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.
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(b) The following functions are positive in quadrant III:
tangent, cotangent
The following functions are negative in quadrant III
cosine, sine, secant, cosecant
A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.
Answer:
Angle BPQ = 64°
Step-by-step explanation:
4x + 12 +2x = 90
6x + 12 = 90
- 12 -12
6x = 78
x = 13°
BPQ = ((4(13) + 12)°
(52 + 12)°
64°
Answer: The largest angle formed during his trip is at the mall between his home and the library.
Step-by-step explanation:
Hi, since the situation forms a right triangle (see image attached) the angle formed between his home and the library is 90°.
The sum of the interior angles of a right triangle is 180°, and the right angle (90°)is the largest angle formed.
So, the largest angle formed during his trip is at the mall between his home and the library.
Feel free to ask for more if needed or if you did not understand something.
