1. Transfer from radians into degrees and from degrees into radians: a) =156 b) =65 ...
1. Transfer from radians into degrees and from degrees into radians: a) α=156∘ b) β=65π 2. Which angle is the same as 98352∘ and in which Quadrant it belongs? 3. Let △ABC be the right triangle. Find all sides and all angles of this triangle if a=4cm and c=8cm. 4. In triangle △ABC find all sides and all angles if α=60∘,β=50∘ and c=10cm. 5. If cosα=52, and α∈IV quadrant. Find sin2α and cos2α.
radian measure = (degree measure × ?)/180StepsStep 1: Plug the angle value, in degrees, in the formula above:radian measure = (156 × ?)/180Step 2: Rearrange the terms:radian measure = ? × 156/180Step 3: Reduce or simplify the fraction of ? if necessaryCalculating the gcd of 156 and 180 [gcd(156,180)], we've found that it equals 12. So, we can simplify this fraction by reducing it to lowest terms:Dividing both numerator and denominator by the gcd 12, we have:? × 156÷12/180÷12 which equals13?/15 radian, after reducing the fraction to lowest terms.Note: 13?/15 rad is the same as:0.86666666666667? radian (as a decimal in terms of ?)2.7227136331112 radian (as a real number)-5?/6 radians is equivalent to -150°. Since ? radians is equal to 180°, we can plug 180° in for ? radians in -5?/6 radians, and then simplify to convert to degrees. We get that -5?/6 radians is equivalent to -150°.