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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 × ?)/180

Steps

Step 1: Plug the angle value, in degrees, in the formula above:

radian measure = (156 × ?)/180

Step 2: Rearrange the terms:

radian measure = ? × 156/180

Step 3: Reduce or simplify the fraction of ? if necessary

Calculating 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 equals

13?/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°.