Back to Exercise: Complementary angle relationship (sin x = cos(90-x))

Complementary Angle Relationship

Grade 10·21 problems·~30 min·Digital SAT Math·topic·sat-geotrig-rt-comp

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Recall / Warm-Up

What is $\\sin(30\degree)$ ?

$\\dfrac{\\sqrt{3}}{2}$

$\\dfrac{1}{2}$

$\\dfrac{\\sqrt{2}}{2}$

$1$

Two acute angles in a right triangle are $A$ and $B$ . What must be true about $A + B$ ?

$A + B = 180\degree$

$A + B = 90\degree$

$A + B = 45\degree$

$A + B = 360\degree$

In a right triangle, the right angle is at vertex $C$ . The two acute angles are $A$ and $B$ , where $B = 90\degree - A$ .
The side opposite $A$ has length 3 and the hypotenuse has length 5.

What is $\cos(B)$ ?

$\\dfrac{4}{5}$

$\\dfrac{3}{5}$

$\\dfrac{3}{4}$

$\\dfrac{5}{3}$

Fluency Practice

If $\\sin(x) = \\cos(35\degree)$ , find $x$ . Enter the value in degrees.

If $\\cos(x) = \\sin(20\degree)$ , find $x$ . Enter the value in degrees.

If $\\sin(x) = \\cos(x + 10\degree)$ , find $x$ . Enter the value in degrees.

Which expression is equivalent to $\\sin(50\degree)$ ?

$\\cos(50\degree)$

$\\sin(40\degree)$

$\\cos(40\degree)$

$\\tan(50\degree)$

If $\\sin(25\degree) = \\cos(y)$ , what is $y$ ?

$155\degree$

$65\degree$

$25\degree$

$115\degree$

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