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Find all degree solutions to the equation s(a-60)=-√3/2.

a) a = 30°
b) a = 90°
c) a = 150°
d) a = 210°

User RRM
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1 Answer

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Final answer:

The degree solutions to the equation s(a-60)=-\sqrt{3}/2 are found by considering where the sine of an angle is -\sqrt{3}/2, which is at angles of 240° and 300°. After adjusting for the (a-60) term, the solutions are 300° and 0°.

Step-by-step explanation:

To find all degree solutions to the equation s(a-60)=-\sqrt{3}/2, we first need to recognize that 's' likely represents the sine function, making the equation sine-related. We can solve for 'a' by using the inverse sine function and considering the unit circle properties where the sine of an angle equals -\sqrt{3}/2.

The angles where sine is -\sqrt{3}/2 are typically in the third and fourth quadrants of the unit circle, corresponding to 240° and 300° respectively. Since the equation involves (a-60), we add 60° to these angles to find the correct values for 'a'. Therefore, a = 240° + 60° = 300° and a = 300° + 60° = 360°. However, since we are looking for the principal angle, the solution 360° is equivalent to 0°.

In conclusion, the possible solutions are a = 300° and a = 0° (equivalent to 360°).

User Prosseek
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