#### Тема: Basic Trigonometric Ratios: Examples - Purplemath

Cheat Sheets & Tables Algebra, Trigonometry and Calculus cheat sheets and a variety of tables. Class Notes Each class has notes available. Most of the classes have.

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Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

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Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

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Index of lessons | Purplemath's lessons in offline form |

Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

DO NOT USE CALCULATOR FOR THESE, YOUR TRIG TEACHER WILL NOT COUNT THEM IF YOU GIVE CALCULATOR RESULTS. ************************************* You should know the unit circle first quadrant by heart for angles 0° with cos 0° = 1. sin 0° = 0 ........√3.... 30° cos 30° = ▬▬ sin30° =1/2 .........2.. ........√2.. 45° cos 45° = ▬ sin45° =√2/2 .........2.. ........1.. 60° cos 60° = ▬ sin60° =√3/2 .........2 90° with cos 90° = 0 sin 0° = 1 cos 15° has to be computed using a half angle formula ........1 + cos x cos² (x/2) = ▬▬▬▬ ..........2 so ........__________ ......../1 + cos 30° cos 15° = \./▬▬▬▬▬ ......√.....2 thus ........__________ ......../1 + √3/2 cos 15° = \./▬▬▬▬▬ ......√.....2 which becomes ........__________ ......../2 + √3 cos 15° = \./▬▬▬▬▬ ......√...4 and that simplifes to .......__________ ......\./2 + √3 cos 15° = ▬▬▬▬▬ .........2 cos 225 degrees That is in the third quadrant just opposite to 45° so ......-√2 cos 225° =▬▬ .......2 Sin 345 degrees That angle is cotermal with -15° and sin -15° = - sin 15° and using a half angle formula as we did for cos 15° ........__________ ......../1 - √3/2 sin 15° = \./▬▬▬▬▬ ......√.....2 so all we have to do for sin -15° is stick a negative sign in front of the radical. That is also the value of sin 345° Sin 75 degrees I ll have you do it yourself. There are two possible ways I: use a half angle formula on 150° or II: use a sum formula on 45° + 30° and the sum formula with sin is sin(x+y) = sin x cos y + cos x sin y

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Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

Demonstrates how to use trig ratios to do simple solving of triangles.

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Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

Varsity Tutors is a live learning platform. Instructors are independent contractors with their own teaching styles, methods, and materials.

Index of lessons | Purplemath''''''''s lessons in offline form |

Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are similar , in the technical sense that their corresponding sides are in proportion. For instance, the following two triangles ( not drawn to scale) have all the same angles, so they are similar, and the corresponding pairs of their sides are in proportion :

TAN(x) = opposite/adjacent = 555/1320 555/1320 = 0.42045 inverse tangent (0.42045) = 22.805 Angle = 22.805 degrees

_________________________________ For the 2nd Quadrant Cosx = -2/3 → x = 131.81° The remaining 5 trig functions are given below. _________________________________ 1) Assuming x is positive and x