Rumus: \(\text{grad} = \frac{\text{derajat}}{360} \times 400\)

\(\text{grad} = \frac{180}{360} \times 400 = 200 \text{ grad}\)

Jawaban: 200 grad

Rumus: \(\text{rad} = \frac{\text{derajat}}{180} \times \pi\)

\(\text{rad} = \frac{90}{180} \times \pi = \frac{\pi}{2}\)

Jawaban: \(\frac{\pi}{2}\) rad

\(45° = 45 \times 60′ = 2700’\)

Jawaban: 2700′

Rumus: \(\text{derajat} = \frac{\text{grad}}{400} \times 360\)

\(\text{derajat} = \frac{200}{400} \times 360 = 180°\)

Jawaban: 180°

Satu putaran penuh = 360° = \(2\pi\) rad ≈ 6,2832 rad

Jawaban: \(2\pi\) rad

\(2°30’36” = 2 + \frac{30}{60} + \frac{36}{3600}\)

\(= 2 + 0{,}5 + 0{,}01 = 2{,}51°\)

Jawaban: 2,51°

\(\text{rad} = \frac{150}{180} \times \pi = \frac{150\pi}{180} = \frac{5\pi}{6}\)

Jawaban: \(\frac{5\pi}{6}\) rad

Derajat: 1°

Sisa: 0,25° × 60 = 15′

Sisa: 0′ → 0″

Jawaban: 1°15’0″

Derajat: \(\frac{75}{400} \times 360 = 67{,}5°\)

Radian: \(\frac{67{,}5}{180} \times \pi = \frac{67{,}5\pi}{180} = \frac{3\pi}{8}\)

Jawaban: 67,5° = \(\frac{3\pi}{8}\) rad

β dalam derajat: \(\frac{100}{400} \times 360 = 90°\)

Karena 120° > 90°, maka α > β.

Jawaban: α = 120° lebih besar

Langkah 1: Ubah ke desimal

\(15°45’30” = 15 + \frac{45}{60} + \frac{30}{3600} = 15 + 0{,}75 + 0{,}00833 = 15{,}7583°\)

Langkah 2: Ubah ke radian

\(\text{rad} = \frac{15{,}7583}{180} \times \pi = 0{,}2750 \text{ rad}\)

Jawaban: 0,2750 rad

Derajat: \(5{,}5 \times 360° = 1980°\)

Radian: \(5{,}5 \times 2\pi = 11\pi \approx 34{,}558 \text{ rad}\)

Gradian: \(5{,}5 \times 400 = 2200 \text{ grad}\)

Jawaban: 1980°, 11π rad, 2200 grad

Derajat desimal: \(\frac{3{,}7}{\pi} \times 180 = \frac{3{,}7 \times 180}{3{,}14159} = 211{,}987°\)

Derajat: 211°

Sisa: 0,987° × 60 = 59,22′ → 59′

Sisa: 0,22′ × 60 = 13,2″ ≈ 13″

Jawaban: 211°59’13”

Dari 12 ke 5 = 5 bagian dari 12 bagian lingkaran penuh.

Derajat: \(\frac{5}{12} \times 360° = 150°\)

Radian: \(\frac{150}{180} \times \pi = \frac{5\pi}{6} \approx 2{,}618 \text{ rad}\)

Gradian: \(\frac{5}{12} \times 400 = 166{,}67 \text{ grad}\)

Jawaban: 150°, \(\frac{5\pi}{6}\) rad, 166,67 grad

Derajat: \(\frac{7\pi}{12} \times \frac{180}{\pi} = \frac{7 \times 180}{12} = 105°\)

DMS: 105°0’0″

Gradian: \(\frac{105}{360} \times 400 = 116{,}67 \text{ grad}\)

Jawaban: 105°0’0″ dan 116,67 grad

\(\text{rad} = \frac{60}{180} \times \pi = \frac{\pi}{3}\)

Jawaban: \(\frac{\pi}{3}\) rad

\(\text{derajat} = \frac{\pi/4}{\pi} \times 180 = \frac{180}{4} = 45°\)

Jawaban: 45°

\(\text{rad} = \frac{30}{180} \times \pi = \frac{\pi}{6}\)

Jawaban: \(\frac{\pi}{6}\) rad

\(\text{derajat} = \frac{\pi}{\pi} \times 180 = 180°\)

Jawaban: 180°

\(\text{rad} = \frac{120}{180} \times \pi = \frac{2\pi}{3}\)

Jawaban: \(\frac{2\pi}{3}\) rad

\(\text{derajat} = \frac{5\pi/4}{\pi} \times 180 = \frac{5 \times 180}{4} = 225°\)

Jawaban: 225°

\(\text{rad} = \frac{210}{180} \times \pi = \frac{210\pi}{180} = \frac{7\pi}{6}\)

Jawaban: \(\frac{7\pi}{6}\) rad

\(\pi\) rad = 180°

Sudut kedua = 180° − 72° = 108°

Jawaban: 108°

\(\text{derajat} = \frac{2}{\pi} \times 180 = \frac{360}{\pi} \approx 114{,}59°\)

Jawaban: 114,59°

\(\text{rad} = \frac{315}{180} \times \pi = \frac{315\pi}{180} = \frac{7\pi}{4}\)

Jawaban: \(\frac{7\pi}{4}\) rad

Ubah 72° ke radian: \(\frac{72}{180} \times \pi = \frac{2\pi}{5}\)

Panjang busur: \(s = r\theta = 10 \times \frac{2\pi}{5} = 4\pi \approx 12{,}57 \text{ cm}\)

Jawaban: \(4\pi \approx 12{,}57\) cm

Luas juring: \(L = \frac{1}{2}r^2\theta = \frac{1}{2}(6)^2 \times \frac{2\pi}{3} = \frac{1}{2} \times 36 \times \frac{2\pi}{3} = 12\pi \approx 37{,}70 \text{ cm}^2\)

Jawaban: \(12\pi \approx 37{,}70 \text{ cm}^2\)

Sudut pelurus: jumlah = \(\pi\) rad

Sudut kedua (radian): \(\pi – \frac{2\pi}{5} = \frac{5\pi – 2\pi}{5} = \frac{3\pi}{5}\)

Sudut kedua (derajat): \(\frac{3\pi/5}{\pi} \times 180 = \frac{3 \times 180}{5} = 108°\)

Jawaban: \(\frac{3\pi}{5}\) rad = 108°

Panjang busur: \(s = r\theta = 50 \times 0{,}8 = 40 \text{ cm}\)

Sudut dalam derajat: \(\frac{0{,}8}{\pi} \times 180 = \frac{144}{\pi} \approx 45{,}84°\)

Jawaban: lintasan = 40 cm, sudut ≈ 45,84°

Ubah radian ke derajat: \(\frac{7\pi}{12} \times \frac{180}{\pi} = \frac{7 \times 180}{12} = 105°\)

Maka: \(3x + 15 = 105\)

\(3x = 90\)

\(x = 30\)

Jawaban: x = 30