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Simple Trig Equations using radians

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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Simple Trig Equations using radians

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  1. Simple Trig Equations using radians

  2. 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 

  3. 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 

  4. 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 , 

  5. 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 , 

  6. 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

  7. 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. , , ,

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