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Simple Trig Equations using radians. Recap: using C.A.S.T. 90°. This diagram tells us the angles where sin, cos and tan (and “all”) give positive results. We measure anti-clockwise from 0 ° EXAMPLE:. . . 0°. 180°. Solve in the interval
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Recap: using C.A.S.T. 90° • This diagram tells us the angles where sin, cos and tan (and “all”) give positive results. • We measure anti-clockwise from 0° • EXAMPLE: 0° 180° • Solve in the interval • Find the principal value (you should know it… if not use with calculator in degree mode) 270° • Value of is positive so solutions are in • Draw acute angle in quadrant and label as • Mark in same acute angle with axis in
Recap: using C.A.S.T. 90° • This diagram tells us the angles where sin, cos and tan (and “all”) give positive results. • We measure anti-clockwise from 0° • EXAMPLE: 0° 180° • Solve in the interval • Find the principal value (you should know it… if not use with calculator in degree mode) 270° • Read off solutions (anti clockwise) • Find extra solutions between and • Solutions: • Value of is positive so solutions are in • Draw acute angle in quadrant and label as • Mark in same acute angle with axis in
Shift-setup “Rad” Status bar will show [R] C.A.S.T. using radians • Useful rules to remember • DEGREES: • RADIANS: 0 / • EXAMPLE • Solve in the interval • Draw CAST diagram and label in radians • Find the principal value (if you can’t remember, use with calcin radian mode) • Read off solutions (clockwise is negative) • Or…find positive solutions (always clockwise) and or to any solutions outside required range • Cos is positive so solutions are in , • Mark in this acute angle with axis in quadrants ,
C.A.S.T. using radians 0 / • EXAMPLE • Solve in the interval • Draw CAST diagram and label in radians • Find the principal value (if you can’t remember, use with calcin radian mode) • Read off solutions (clockwise is negative) • Or…find positive solutions (always clockwise) and or to any solutions outside required range • Cos is positive so solutions are in , • Mark in this acute angle with axis in quadrants ,
Slideshow available on mrstevenson maths C.A.S.T. using radians • Within the range give all values of for which • Find the smallest angle (positive or negative) for which • and • and 0.412, 2.73, -3.55, -5.87
Slideshow available on mrstevenson maths C.A.S.T. using radians • Within the range give all values of for which • Find the smallest angle (positive or negative) for which • and • and Answers in radians to 3 s.f. , , ,