# Finding Values on the Calculator - White Plains Public Schools

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Writing Trigonometric RatiosWarm-UpA trigonometric ratio is a ratio of two sides of a right triangle. We can use trigonometric ratios to relate the angles of a triangle to the lengths of the triangle’s sides. In a right triangle, three relationships exist which relate the angles of a triangle to the measures of its sides.The word opposite means _________________________________________________The word adjacent means _________________________________________________The hypotenuse is _______________________________________________________-295275-3810sine (sin) of Angle x = Side Opposite to Angle xHypotenusecosine (cos) of Angle x = Side Adjacent to Angle xHypotenusetangent (tan) of Angle x = Side Opposite to Angle xSide Adjacent to Angle xWe write: sinx= opp xhypcosx= adj xhyptanx= opp xadj xRemember this!----------------------------------------> Remember to label all sides first:OPPOSITE, ADJACENT, HYPOTENUSEExample2722245299085For the given triangle, express as a fraction:sin Acos Atan A2722245299085For the given triangle, express as a fraction:sin BSides OPPOSITE and ADJACENT will change depending on which angle you’re talking about. e) cos B f) tan BExpress each of the above as a decimal rounded to the nearest ten-thousandth:sin B = _______________ cos B = ___________________ tan B = _______________The HYPOTENUSE will always be across from the right angle. So label it first!ExerciseFor the given triangle, express as a fraction:337185022225sin Kcos Ktan K337185073660sin Jcos Jtan JFor the given triangle, express as a fraction and a decimal rounded to the nearest ten-thousandth:348615064770cos Ltan Lsin L356235010160sin Mtan Mcos MFinding Values on the CalculatorThe sine, cosine, and tangent of any angle is a known value that can be found using any scientific calculator.ExamplesUsing your calculator, find the value of each to the nearest ten-thousandth:sin 38° _______________ cos 38° _______________tan38° ___________________ExerciseUsing your calculator, find the value of each to the nearest ten-thousandth:tan 22° _______________ cos 17° _______________tan31° ___________________sin 80° _______________ sin 42° _______________cos60° ___________________sin 45° _______________tan 65° _______________cos44° ___________________Lesson SummaryThe Three Trigonometric Ratiossinx= opp xhypcosx= adj xhyptanx= opp xadj xExit ticketHomeworkExpress each ratio indicated as a fraction.Finding a Missing Side Length Using the Trigonometric RatiosWarm-UpThe trigonometric ratios can help us to solve for a missing side in a right triangle.sinx= opp xhypcosx= adj xhyptanx= opp xadj x262890087630Example #1Find, to the nearest tenth:ABACExample #23448050167005Find, to the nearest tenth:MPNM Exercise3514725153035Find, to the nearest tenth: XYYZFind, to the nearest tenth:36861753810DEDF3829050-219075Find, to the nearest tenth:TUTVSolving Problems Using Trigonometric RatiosModel Problem-552450-3175Exercise-15240012703) Find KL. 4) Find GH and HJ.Lesson SummaryLabel the sides of the triangle, OPPOSITE, ADJACENT, and HYPOTENUSE.Using SOH-CAH-TOA, determine which trig ratio to use in the problem.Set up the trig ratio using the formula.Cross-multiply and solve.Exit TicketFind JL.600075144780Homework952502609857) Find TV and TU.402907542545180975425452) 3) 180975-635 Finding a Missing Angle When the Side Lengths are KnownWarm-UpFinding Missing Angle Measures Using Inverse FunctionsIf you know the sine, cosine, or tangent of an acute angle measure, you can use the inverse trigonometric functions to find the measure of the angle.We say “sine inverse”Example #1Find sin35° ___________________________ Find sin-1(.573576) _________________Find cos18° ___________________________ Find cos-1(.951056) _________________Find tan22° ___________________________ Find sin-1(.404026) _________________What does the inverse function do? _____________________________________Example #2Find the measure of angle A if:sin A = 0.3456tan A = 1.4552cos A = 0.4995Example #33505200128270Find the measure of angle A to the nearest degree.Guided Practice39624014445Find the measure of angle P to the nearest degree. Practice Find each angle measure to the nearest degree.Find m∠R. 2) Find m∠B.2381251568453257550768353838575478155-2095504114803) Find m∠F. 4) Find m∠R.Solving Word ProblemsModel Problem-504825102235Exercise-114300179070Homework-2381251289052762252603513) ................
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