Trigonometry - SAT Math
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Question
What is the sine of a $45^\text{°}$ angle in a right triangle?
What is the sine of a $45^\text{°}$ angle in a right triangle?
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Answer
$\frac{\text{√}2}{2}$. In a 45-45-90 triangle, opposite and adjacent sides are equal.
$\frac{\text{√}2}{2}$. In a 45-45-90 triangle, opposite and adjacent sides are equal.
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Question
State the Pythagorean identity involving sine and cosine.
State the Pythagorean identity involving sine and cosine.
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Answer
$\text{sin}^2\theta + \text{cos}^2\theta = 1$. Fundamental trigonometric identity derived from the unit circle.
$\text{sin}^2\theta + \text{cos}^2\theta = 1$. Fundamental trigonometric identity derived from the unit circle.
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Question
Identify the reciprocal function of sine.
Identify the reciprocal function of sine.
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Answer
Cosecant (csc). Since $\sin\theta = \frac{1}{\csc\theta}$, cosecant is sine's reciprocal.
Cosecant (csc). Since $\sin\theta = \frac{1}{\csc\theta}$, cosecant is sine's reciprocal.
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Question
What is the value of $\text{cos} 0^\text{°}$?
What is the value of $\text{cos} 0^\text{°}$?
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Answer
- At 0°, the point on the unit circle is (1,0), so cosine equals 1.
- At 0°, the point on the unit circle is (1,0), so cosine equals 1.
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