By the mnemonic ASTC, you will recall that the cosine function is positive in QI and QIV. So, we are looking for an angle in QIV that has a reference angle of 54°. So that angle is 306°. (In general, any two angles that add to 360° will share a cosine value.)
For sine, which is positive in QI and QII, we need the QII angle with a reference angle of 54°, which is 126°. (In general, any two angles that sum to 180° will have the same sine value. Also angles that sum to 540°, for angles with negative sine values, in QIII and QIV.)
reference angle: the positive acute angle formed by an angle’s terminal ray and the x-axis, in general, any angles with the same reference angle will have trig values of equal magnitude (the same, ignoring signs)
