MA 154 Lesson 6 Delworth
Section 6.4 Values of Trigonometric Functions
Definition of Reference Angle: Let q be a nonquadrantal angle in standard position. The reference angle of q is the acute angle qR that the terminal side of q makes with the x-axis.
If q is in QI, qR = q
If q is in QII, qR = 180° – q or p – q
If q is in QIII, qR = q – 180° or q – p
If q is in QIV, qR = 360° – q or 2p – q
Find the reference angle qR.
q = 132° q = 236° q = 311° q = –120°
:
q = 1.2 q = 2.3 q = 3.6 q = 5.6
Find the exact value.
Approximate to three decimal places.
is only defined in the 1st and 2nd quadrants. When you use the inv. cos key on your calculator it will always return either a positive (1st quadrant) or a positive (2nd quadrant) angle.
is only defined in the 1st and 4th quadrants. When you use the inv. sin key on your calculator it will always return either a positive (1st quadrant) or a negative (4th quadrant) angle.
is the same as and is only defined in the 1st and 4th quadrants. When you use the inv. tan key on your calculator it will always return either a positive (1st quadrant) or a negative (4th quadrant) angle.
Approximate the acute angle q to the nearest a) 0.01° and b) 1'
cosq = 0.3456 tanq = 1.9064
Approximate to the nearest 0.1°, all angles q in the interval [0°, 360°) that satisfy the equation.
sinq = 0.4567 tanq = -1.4826 secq = 1.4080
cosq = –0.4617 cotq = 2.4586 cscq = –2.5896
Approximate to the nearest 0.01 radians, all angles q in the interval [0, 2p) that satisfy the equation.
cosq = 0.2314 cotq = – 0.5241 cscq = 1.2665
sinq = –0.9852 tanq = 5.2683 secq = –2.7514
Definition of Reference Angle: Let q be a nonquadrantal angle in standard position. The reference angle of q is the acute angle qR that the terminal side of q makes with the x-axis.
If q is in QI, qR = q
If q is in QII, qR = 180° – q or p – q
If q is in QIII, qR = q – 180° or q – p
If q is in QIV, qR = 360° – q or 2p – q
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