Determine two angles between 0°and 360°that have a secant of -4. Round your answers to the nearest degree.
There are tw answer 104°( I got this one but there is also 256° I don't have anyidea for this one please explain to me
I appreciate your time thankyou sooo much!!!
To determine angles between 0° and 360° that have a secant of -4, you can follow these steps:
1. Recall that the secant is the reciprocal of the cosine function.
2. Use the fact that secant is equal to -4 to find the cosine value. Since secant is the reciprocal of cosine, cosine will be equal to 1 divided by -4, which is -1/4.
3. To find the first angle, use the inverse cosine function (also known as arccosine) to find the principal angle whose cosine is -1/4. This can be done using a scientific calculator or an online trigonometric calculator. The arccosine of -1/4 is approximately 104°.
4. To find the second angle, subtract the first angle from 360° to obtain the reference angle in the fourth quadrant. In this case, it would be 360° - 104° = 256°.
5. Recognize that the cosine function has the same value in the first and fourth quadrants, so the angle in the fourth quadrant will also have a cosine of -1/4 (and hence a secant of -4).
Therefore, the two angles between 0° and 360° that have a secant of -4 are approximately 104° and 256°.