SATMathematics Practice Test 1

By the complementary angle relationship for sine and cosine, $\sin(x^{\circ}) = \cos(90^{\circ} - x^{\circ})$. Therefore, $\cos(90^{\circ} - x^{\circ}) = \frac{4}{5}$ . Either the fraction $\frac{4}{5}$ or its decimal equivalent, 0.8, may be gridded as the correct answer Alternatively, one can construct a right triangle that has an angle of measure $x^{\circ}$ such that $\sin(x^{\circ}) = \frac{4}{5}$, as shown in the figure below, where $\sin(x^{\circ})$ is equal to the ratio of the opposite side to the hypotenuse, or $\frac{4}{5}$ Since two of the angles of the triangle are of measure x° and 90°, the third angle must have the measure $180^{\circ} - 90^{\circ} - x^{\circ} = 90^{\circ} - x^{\circ}$. From the figure, $\cos(90^{\circ} - x^{\circ})$, which is equal to the ratio of the adjacent side to the hypotenuse, is also $\frac{4}{5}$ .